Is action complexity better for de Sitter space in Jackiw-Teitelboim gravity?

Volume complexity in dS remains O(1) up to a critical time, after which it suddenly diverges. On the other hand, for the dS solution in JT gravity, there is a linear dilaton which smoothly grows towards the future infinity. From the dimensional reduction viewpoint, the growth of the dilaton is due to the expansion of the orthogonal sphere in higher-dimensional dS (d ≥ 3). Since in higher dimensions complexity becomes very large even before the critical time, by properly taking into account the dilaton, the same behavior is expected for complexity in dS JT gravity. We show that this expectation is met by the complexity = action (CA) conjecture. For this purpose, we obtain an appropriate action for dS in JT gravity, by dimensional reduction from dS. In addition, we discuss complexity = “refined volume” where we choose an appropriate Weyl field-redefinition such that refined volume avoids the discontinuous jump in time evolution.